Question

# Is the national crime rate really going down? Some sociologists say yes! They say that the...

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 33 arrests last month, 20 were of males aged 15 to 34 years. Use a 5% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.

(a) What is the level of significance?

State the null and alternate hypotheses. a) H0: p = 0.7; H1: p ≠ 0.7 b) H0: p ≠ 0.7; H1: p = 0.7 c) H0: p = 0 .7; H1: p < 0.7 d)H0: p = 0.7; H1: p > 0.7 H0: p < 0 .7; H1: p = 0.7

(b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. The Student's t, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Solution :-

Given that ,

n = 33

x = 20

(a) What is the level of significance

0.05

The null and alternative hypothesis is

H0 : p = 0.7

Ha : p 0.7

This is the two tailed test .

= x / n = 20 / 33 = 0.6061

P0 = 70% = 0.7

1 - P0 = 1 - 0.7 = 0.30

(b) What sampling distribution will you use? The standard normal, since np < 5 and nq < 5.

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.6061 - 0.7 / [0.7 ( 1 - 0.7 ) / 33 ]

= -1.178

The test statistic = -1.18

P-value = 0.2380